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Optimal low-thrust trajectories for the direct escape from the Earth’s sphere of influence, starting from Sun-Earth or Earth-Moon L2, are analyzed with an indirect optimization method. The dynamic model considers four-body gravitation and JPL ephemeris; solar radiation pressure is also considered. Specific techniques and improvements to the method are introduced to tackle the highly chaotic and nonlinear dynamics of motion close to Lagrangian points, which challenges the remarkable precision of the indirect method. The results show that escape trajectories have optimal performance when the solar perturbation acts favorably in both thrust and coast phases. The effects of the solar and Moon perturbations are more evident in the Earth-Moon L2 escapes compared with those from the Sun-Earth L2. EML2 escapes have single- or two-burn solutions depending on the trajectory deflection, which is needed to have a favorable solar perturbation. The SEL2 escapes, on the contrary, mainly have a single initial burn and a long coast arc, but need an additional final thrust arc if the required C3 is high. As applications of such Lagrangian Point trajectories, results include considerations about escape maneuvers from different SEL2 high-fidelity Lyapunov orbits and escape for interplanetary trajectories towards near-earth asteroids.

Optimal Escape from Sun-Earth and Earth-Moon L2 with Electric Propulsion